The use of capacitors with temperature dependent dielectric constants to convert heat to electric energy is well known. Representative devices that use dielectrics as variable capacitors to generate electricity are disclosed, for example, in U.S. Pat. No. 4,220,906 to Drummond, U.S. Pat. Nos. 4,425,540 and 4,647,836 to Olsen, U.S. Pat. No. 6,528,898 to Ikura et al. and U.S. Pat. No. 7,323,506 to Kouchachvili et al. Those devices simply utilize the fact that the dielectric constant of certain materials, such as ferroelectrics, varies as temperature varies. Specifically, those devices use the dielectrics as temperature dependent variable capacitors, the capacitance of which decreases as the temperature is increased by the absorption of heat. The capacitor is partially charged under an applied field at the lower temperature, and is then fully charged by increasing the electric field. The capacitor is then heated while under that large field, and it partially discharges as the dielectric constant decreases with increasing temperature and correspondingly decreasing capacitance. Further discharge occurs by reducing the applied field while the capacitor remains at high temperature. (U.S. Pat. No. 4,425,540 to Olsen). Such cycling of the temperature and dielectric constant of a capacitor under an applied field is referred to as the Olsen cycle.
The physics of the capacitor device is straightforward. The voltage V of a capacitor of capacitance C is inversely proportional to the dielectric constant ∈:V=Q/C=Q/[∈(T)∈0(A/d)]After the capacitor has been fully charged by application of the external field under the Olsen cycle, the capacitor is heated to a temperature at which the dielectric constant, ∈, decreases. During that heating leg of the Olsen cycle, partial discharge occurs because the charge, Q, held by the capacitor decreases while V is held constant.
The use of dielectrics as variable capacitors to generate electricity is also reported by Olsen in Cascaded Pyroelectric Converter, 59 FERROELECTRICS 205 (1984). Olsen reports a maximum power density of 33 W/L (about 4 W/kg) using the ferroelectric PZST as the dielectric material in a variable capacitor device with multiple stages and regeneration. Using finite element simulation, Vanderpool calculates that the Olsen cycle yields a power density of 24 W/L (about 3 W/kg) under certain conditions using PZST as the dielectric material in a variable capacitor. Vanderpool, Simulations of a Prototypical Device Using Pyroelectric Materials for Harvesting Waste Heat, 51 INT. J. HT & MASS TRANSFER 5051 (2008).
The variable capacitor method of converting heat to electricity is not the most effective method of using ferroelectrics to generate electricity, however. True pyroelectric generation focuses, instead, on the inherent polarization that occurs in the ferroelectric phase, independent of polarization induced by an applied field. That inherent polarization provides a much more robust source of electric energy. Variable capacitors do not effectively exploit the powerful inherent spontaneous polarization that occurs in ferroelectrics without an applied field. Further, the application of large external fields and the continuous application of an external field during cycling impede the more powerful energy conversion that can be achieved with ferroelectrics. Such external fields prevent the effective use of the tremendous electrical energy that arises from the electric dipoles of ferroelectric materials spontaneously and without induction by an external field.
Therefore, a heretofore unaddressed need exists in the art to address the aforementioned deficiencies and inadequacies.